---
title: "BayLum: An Introduction"
author: "Claire Christophe, Anne Philippe, Sebastian Kreutzer, Guillaume Guérin, Frederik Baumgarten"
date: 'Updated for BayLum package version 0.3.2 (2024-09-18)'
output:
rmarkdown::html_vignette:
toc: yes
toc_depth: 4
number_sections: yes
vignette: >
%\VignetteIndexEntry{BayLum: An Introduction}
%\VignetteEngine{knitr::rmarkdown}
%\VignetteEncoding{UTF-8}
---
# Introduction
`'BayLum'` provides a collection of various **R** functions for Bayesian analysis of luminescence data.
Amongst others, this includes data import, export, application of age models and palaeodose modelling.
Data can be processed simultaneously for various samples, including the input of multiple BIN/BINX-files per
sample for single grain (SG) or multi-grain (MG) OSL measurements. Stratigraphic constraints and
systematic errors can be added to constrain the analysis further.
For those who already know how to use **R**, `'BayLum'` won't be difficult to use,
for all others, this brief introduction may be of help to make the first steps with **R** and
the package `'BayLum'` as convenient as possible.
## Installing `BayLum' package
If you read this document before having installed **R** itself, you should first visit the
[R project](https://www.r-project.org) website and download and install **R**.
You may also consider installing [Rstudio](https://posit.co),
which provides an excellent desktop working environment for **R**; however it is not
a prerequisite.
You will also need the external software *JAGS* (Just Another Gibs Sampler).
Please visit the [JAGS](https://mcmc-jags.sourceforge.io) webpage and follow the installation instructions.
Now you are nearly ready to work with 'BayLum'.
If you have not yet installed 'BayLum', please run the following two **R** code lines to
install 'BayLum' on your computer.
``` r
install.packages("BayLum", dependencies = TRUE)
```
Alternatively, you can load an already installed **R** package (here 'BayLum') into your session by using
the following **R** call.
``` r
library(BayLum)
```
# First steps: age analysis of one sample
Measurement data can be imported using two different options as detailed in the following:
* Option 1: Using the conventional 'BayLum' folder structure (old)
* Option 2: Using a single-setting config file (new)
## Option 1: Import information from a BIN/BINX-file.
Let us consider the sample named *samp1*, which is the example dataset coming with the package.
All information related to this sample is stored in a subfolder called also *samp1*.
To test the package example, first, we add the path of the example
dataset to the object `path`.
``` r
path <- paste0(system.file("extdata/", package = "BayLum"), "/")
```
Please note that for your own dataset (i.e. not included in the package)
you have to replace this call by something like:
``` r
path <- "Users/Master_of_luminescence/Documents/MyFamousOSLData"
```
In our example the folder contains the following subfolders and files:
| | |
|:--|:-------------------------|
|1 |example.yml |
|2 |FER1/bin.bin |
|3 |FER1/Disc.csv |
|4 |FER1/DoseEnv.csv |
|5 |FER1/DoseSource.csv |
|6 |FER1/rule.csv |
|7 |samp1/bin.bin |
|8 |samp1/DiscPos.csv |
|9 |samp1/DoseEnv.csv |
|10 |samp1/DoseSource.csv |
|11 |samp1/rule.csv |
|12 |samp2/bin.bin |
|13 |samp2/DiscPos.csv |
|14 |samp2/DoseEnv.csv |
|15 |samp2/DoseSource.csv |
|16 |samp2/rule.csv |
|17 |yaml_config_reference.yml |
See *"What are the required files in each subfolder?"* in the manual of `Generate_DataFile()` function
for the meaning of these files.
To import your data, simply call the function `Generate_DataFile()`:
``` r
DATA1 <-
Generate_DataFile(
Path = path,
FolderNames = "samp1",
Nb_sample = 1,
verbose = FALSE)
```
```
Warning in Generate_DataFile(Path = path, FolderNames = "samp1", Nb_sample = 1, : 'Generate_DataFile' est obsolète.
Utilisez plutôt ‘create_DataFile()’.
Voir help("Deprecated")
```
### Remarks
#### Data import/export
The import may take a while, in particular for large BIN/BINX-files. This can become annoying if you want to play with the data.
In such situations, it makes sense to save your imported data somewhere else before continuing.
To save the obove imported data on your hardrive use
``` r
save(DATA1, file = "YourPath/DATA1.RData")
```
To load the data use
``` r
load(DATA1, file = "YourPath/DATA1.RData")
```
#### Data structure
To see the overall structure of the data generated from the BIN/BINX-file and the associated CSV-files,
the following call can be used:
``` r
str(DATA1)
```
```
List of 9
$ LT :List of 1
..$ : num [1, 1:7] 2.042 0.842 1.678 3.826 4.258 ...
$ sLT :List of 1
..$ : num [1, 1:7] 0.344 0.162 0.328 0.803 0.941 ...
$ ITimes :List of 1
..$ : num [1, 1:6] 15 30 60 100 0 15
$ dLab : num [1:2, 1] 1.53e-01 5.89e-05
$ ddot_env : num [1:2, 1] 2.512 0.0563
$ regDose :List of 1
..$ : num [1, 1:6] 2.3 4.6 9.21 15.35 0 ...
$ J : num 1
$ K : num 6
$ Nb_measurement: num 16
```
It reveals that `DATA1` is basically a list with 9 elements:
Element | Content |
---------------------- |---------------
`DATA1$LT` | $L_x$/$T_x$ values from each sample |
`DATA1$sLT` | $L_x$/$T_x$ error values from each sample |
`DATA1$ITimes` | Irradiation times |
`DATA1$dLab` | The lab dose rate |
`DATA1$ddot_env` | The environmental dose rate and its variance |
`DATA1$regDose` | The regenerated dose points |
`DATA1$J` | The number of aliquots selected for each BIN-file |
`DATA1$K` | The number of regenerated dose points |
`DATA1$Nb_measurement` | The number of measurements per BIN-file |
#### Visualise Lx/Tx values and dose points
To get an impression on how your data look like, you can visualise them by
using the function `LT_RegenDose()`:
``` r
LT_RegenDose(
DATA = DATA1,
Path = path,
FolderNames = "samp1",
SampleNames = "samp1",
Nb_sample = 1,
nrow = NULL
)
```
```
Warning in LT_RegenDose(DATA = DATA1, Path = path, FolderNames = "samp1", : 'LT_RegenDose' est obsolète.
Utilisez plutôt ‘plot_RegDosePoints()’.
Voir help("Deprecated")
```
Note that here we consider only one sample, and the name of the folder is the name of the sample.
For that reason the argumetns were set to `FolderNames = samp1` and `SampleNames = samp1`.
### Generate data file from BIN/BINX-files of multi-grain OSL measurements
For a multi-grain OSL measurements, instead of `Generate_DataFile()`, the function `Generate_DataFile_MG()` should
be used with similar parameters. The functions differ by their expectations: *Disc.csv* instead of *DiscPos.csv* file for Single-grain OSL Measurements.
Please check type `?Generate_DataFile_MG` for further information.
## Option 2: Import data using `create_DataFile()`
With `'BayLum'` >= v0.3.2 we introduced a new function called `create_DataFile()`, which
will at some point in time replace the function `Generate_DataFile()` and `Generate_DataFile_MG()`.
`create_DataFile()` works conceptionally very different from the approach detailed above.
Key differences are:
* The function uses a single configuration file for all samples and all measurement files
* The very error prone subfolder structure is no longer needed
* Measurement data can be imported with `create_DataFile()`, but also outside of the function
and then passed on the functions. This enables the possibility of extensive pre-processing
and selection of measurement data.
The configuration follows the so-called [YAML format](https://yaml.org) specification.
For single sample the file looks as follows:
```
- sample: "samp1"
files: null
settings:
dose_source: { value: 0.1535, error: 0.00005891 }
dose_env: { value: 2.512, error: 0.05626 }
rules:
beginSignal: 6
endSignal: 8
beginBackground: 50
endBackground: 55
beginTest: 6
endTest: 8
beginTestBackground: 50
endTestBackground: 55
inflatePercent: 0.027
nbOfLastCycleToRemove: 1
```
In the case above, the configuration file assumes that data for `samp1` are
already imported and treated and a R object called `samp1` is available in the global
environment. The following example code reproduces this case:
``` r
## get example file path from package
yaml_file <- system.file("extdata/example.yml", package = "BayLum")
samp1_file <- system.file("extdata/samp1/bin.bin", package = "BayLum")
## read YAML manually and select only the first record
config_file <- yaml::read_yaml(yaml_file)[[1]]
## import BIN/BINX files and select position 2 and grain 32 only
samp1 <- Luminescence::read_BIN2R(samp1_file, verbose = FALSE) |>
subset(POSITION == 2 & GRAIN == 32)
## create the data file
DATA1 <- create_DataFile(config_file, verbose = FALSE)
```
## Age computation
To compute the age of the sample *samp1*, you can run the following code:
``` r
Age <- Age_Computation(
DATA = DATA1,
SampleName = "samp1",
PriorAge = c(10, 100),
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
Iter = 10000
)
```
```
Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 6
Unobserved stochastic nodes: 9
Total graph size: 139
Initializing model
```
```
>> Sample name <<
----------------------------------------------
samp1
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Point estimate Uppers confidence interval
A 1.043 1.102
D 1.042 1.098
sD 1.036 1.058
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
parameter Bayes estimate Credible interval
----------------------------------------------
A 25.061
lower bound upper bound
at level 95% 10 50.294
at level 68% 10 21.841
----------------------------------------------
D 62.212
lower bound upper bound
at level 95% 19.675 125.768
at level 68% 22.385 55.487
----------------------------------------------
sD 44.674
lower bound upper bound
at level 95% 0.15 126.445
at level 68% 0.263 28.94
```
This also works if `DATA1` is the output of `Generate_DataFile_MG()`.
##### Remark 1: MCMC trajectories
- If MCMC trajectories did not converge, you can add more iteration with the parameter `Iter` in the function `Age_Computation()`,
for example `Iter = 20000` or `Iter = 50000`. If it is not desirable to re-run the model from scratch, read the
- To increase the precision of prior distribution, if not specified before you can use the argument `PriorAge`.
For example: `PriorAge= c(0.01,10)` for a young sample and `PriorAge = c(10,100)` for an old sample.
- If the trajectories are still not convergering, you should whether the choice you made with the argument `distribution` and
dose-response curves are meaningful.
##### Remark 2: `LIN_fit` and `Origin_fit`, dose-response curves option
- By default, a saturating exponential plus linear dose response curve is expected. However, you choose other formula by changing arguments
`LIN_fit` and `Origin_fit` in the function.
##### Remark 3: `distribution`, equivalent dose dispersion option
By default, a *cauchy* distribution is assumed, but you can choose another distribution by replacing the
word `cauchy` by `gaussian`, `lognormal_A` or `lognormal_M` for the argument `distribution`.
The difference between the models: *lognormal_A* and *lognormal_M* is that the equivalent dose dispersion
are distributed according to:
- a log-normal distribution with mean or average equal to the palaeodose for the first model
- a log-normal distribution with median equal to the palaeodose for the second model.
##### Remark 4: `SavePdf` and `SaveEstimates` option
These two arguments allow to save the results to files.
- `SavePdf = TRUE` create a PDF-file with MCMC trajectories of parameters `A` (age), `D` (palaeodose), `sD` (equivalent doses dispersion).
You have to specify `OutputFileName` and `OutputFilePath` to define name and path of the PDF-file.
- `SaveEstimates = TRUE` saves a CSV-file containing the Bayes estimates, the credible interval at 68\% and 95\% and the Gelman and Rudin test of
convergence of the parameters `A`, `D`, `sD`. For the export the arguments `OutputTableName` and `OutputTablePath` have to be specified.
##### Remark 4: `PriorAge` option
By default, an age between 0.01 ka and 100 ka is expected.
If the user has more informations on the sample, `PriorAge` should be modified accordingly.
For example, if you know that the sample is an older, you can set `PriorAge=c(10,120)`. In contrast, if you know that the sample is younger,
you may want to set `PriorAge=c(0.001,10)`. Ages of $<=0$ are not possible. The minimum bound is 0.001.
**Please note that the setting of `PriorAge` is not trivial, wrongly set boundaries are likely biasing
your results.**
## Multiple BIN/BINX-files for one sample
In the previous example we considered only the simplest case: one sample, and one BIN/BINX-file.
However, 'BayLum' allows to process multiple BIN/BINX-files for one sample.
To work with multiple BIN/BINX-files, the names of the subfolders need to beset in argument `Names` and
both files need to be located unter the same `Path`.
For the case
``` r
Names <- c("samp1", "samp2")
```
the call `Generate_DataFile()` (or `Generate_DataFile_MG()`) becomes as follows:
``` r
##argument setting
nbsample <- 1
nbbinfile <- length(Names)
Binpersample <- c(length(Names))
##call data file generator
DATA_BF <- Generate_DataFile(
Path = path,
FolderNames = Names,
Nb_sample = nbsample,
Nb_binfile = nbbinfile,
BinPerSample = Binpersample,
verbose = FALSE
)
```
```
Warning in Generate_DataFile(Path = path, FolderNames = Names, Nb_sample = nbsample, : 'Generate_DataFile' est obsolète.
Utilisez plutôt ‘create_DataFile()’.
Voir help("Deprecated")
```
``` r
##calculate the age
Age <- Age_Computation(
DATA = DATA_BF,
SampleName = Names,
BinPerSample = Binpersample
)
```
```
Compiling model graph
Resolving undeclared variables
Allocating nodes
Graph information:
Observed stochastic nodes: 12
Unobserved stochastic nodes: 15
Total graph size: 221
Initializing model
```
```
>> Sample name <<
----------------------------------------------
samp1 samp2
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Point estimate Uppers confidence interval
A 1.018 1.023
D 1.022 1.027
sD 1.044 1.057
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
parameter Bayes estimate Credible interval
----------------------------------------------
A 2.312
lower bound upper bound
at level 95% 0.86 3.819
at level 68% 1.65 2.728
----------------------------------------------
D 5.75
lower bound upper bound
at level 95% 2.602 9.545
at level 68% 4.453 6.886
----------------------------------------------
sD 0.881
lower bound upper bound
at level 95% 0.003 3.318
at level 68% 0.003 0.846
```
# Age analysis of various samples
## Generate data file from BIN/BINX-files
The function `Generate_DataFile()` (or `Generate_DataFile_MF()`) can process multiple files
simultaneously including multiple BIN/BINX-files per sample.
We assume that we are interested in two samples named: *sample1* and *sample2*. In addition, we have
two BIN/BINX-files for the first sample named: *sample1-1* and *sample1-2*, and one BIN-file for the 2nd sample named *sample2-1*.
In such case, we need three subfolders named *sample1-1*, *sample1-2* and *sample2-1*;
which each subfolder containing only one BIN-file named **bin.bin**, and its associated files **DiscPos.csv**, **DoseEnv.csv**, **DoseSourve.csv** and **rule.csv**.
All of these 3 subfolders must be located in *path*.
To fill the argument corectly `BinPerSample`: $binpersample=c(\underbrace{2}_{\text{sample 1: 2 bin files}},\underbrace{1}_{\text{sample 2: 1 bin file}})$
``` r
Names <-
c("sample1-1", "sample1-2", "sample2-1") # give the name of the folder datat
nbsample <- 2 # give the number of samples
nbbinfile <- 3 # give the number of bin files
DATA <- Generate_DataFile(
Path = path,
FolderNames = Names,
Nb_sample = nbsample,
Nb_binfile = nbbinfile,
BinPerSample = binpersample
)
```
### Combine files using the function `combine_DataFiles()`
If the user has already saved informations imported with `Generate_DataFile()` function (or `Generate_DataFile_MG()` function)
these data can be concatenate with the function `combine_DataFiles()`.
For example, if `DATA1` is the output of sample named "GDB3", and `DATA2` is the output of sample "GDB5",
both data can be merged with the following call:
``` r
data("DATA1", envir = environment())
data("DATA2", envir = environment())
DATA3 <- combine_DataFiles(L1 = DATA2, L2 = DATA1)
str(DATA3)
```
```
List of 11
$ LT :List of 2
..$ : num [1:188, 1:6] 4.54 2.73 2.54 2.27 1.48 ...
..$ : num [1:101, 1:6] 5.66 6.9 4.05 3.43 4.97 ...
$ sLT :List of 2
..$ : num [1:188, 1:6] 0.333 0.386 0.128 0.171 0.145 ...
..$ : num [1:101, 1:6] 0.373 0.315 0.245 0.181 0.246 ...
$ ITimes :List of 2
..$ : num [1:188, 1:5] 40 40 40 40 40 40 40 40 40 40 ...
..$ : num [1:101, 1:5] 160 160 160 160 160 160 160 160 160 160 ...
$ dLab : num [1:2, 1:2] 1.53e-01 5.89e-05 1.53e-01 5.89e-05
$ ddot_env : num [1:2, 1:2] 2.512 0.0563 2.26 0.0617
$ regDose :List of 2
..$ : num [1:188, 1:5] 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14 6.14 ...
..$ : num [1:101, 1:5] 24.6 24.6 24.6 24.6 24.6 ...
$ J : num [1:2] 188 101
$ K : num [1:2] 5 5
$ Nb_measurement: num [1:2] 14 14
$ SampleNames : chr [1:2] "samp 1" "samp 1"
$ Nb_sample : num 2
- attr(*, "originator")= chr "create_DataFile"
```
The data structure should become as follows
- 2 `list`s (1 `list` per sample) for `DATA$LT`, `DATA$sLT`, `DATA1$ITimes` and `DATA1$regDose`
- A `matrix` with 2 columns (1 line per sample) for `DATA1$dLab`, `DATA1$ddot_env`
- 2 `integer`s (1 `integer` per BIN files here we have 1 BIN-file per sample) for `DATA1$J`, `DATA1$K`, `DATA1$Nb_measurement`.
Single-grain and multiple-grain OSL measurements can be merged in the same way.
To plot the $L/T$ as a function of the regenerative dose the function `LT_RegenDose()` can be
used again:
``` r
plot_RegDosePoints(DATA3)
```
*Note: In the example `DATA3` contains information from the samples 'GDB3' and 'GDB5', which are single-grain OSL measurements. For a correct treatment the argument `SG` has to be manually set by the user. Please see the function manual for further details.*
## Age analysis without stratigraphic constraints
If no stratigraphic constraints were set, the following code can be used to analyse the age of the sample *GDB5* and *GDB3* simultaneously.
``` r
priorage = c(1, 10, 10, 100)
Age <- AgeS_Computation(
DATA = DATA3,
Nb_sample = 2,
SampleNames = c("GDB5", "GDB3"),
PriorAge = priorage,
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
Iter = 1000,
jags_method = "rjags"
)
```
```
Warning: No initial values were provided - JAGS will use the same initial values for all chains
```
```
Compiling rjags model...
Calling the simulation using the rjags method...
Adapting the model for 1000 iterations...
Running the model for 5000 iterations...
Simulation complete
Calculating summary statistics...
Calculating the Gelman-Rubin statistic for 6 variables....
Finished running the simulation
```
```
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Sample name: GDB5
---------------------
Point estimate Uppers confidence interval
A_GDB5 1.002 1.005
D_GDB5 1.003 1.012
sD_GDB5 1.006 1.021
----------------------------------------------
Sample name: GDB3
---------------------
Point estimate Uppers confidence interval
A_GDB3 1 1
D_GDB3 1.001 1.002
sD_GDB3 1.001 1.005
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
>> Bayes estimates of Age, Palaeodose and its dispersion for each sample and credible interval <<
----------------------------------------------
Sample name: GDB5
---------------------
Parameter Bayes estimate Credible interval
A_GDB5 7.132
lower bound upper bound
at level 95% 5.783 8.596
at level 68% 6.298 7.677
Parameter Bayes estimate Credible interval
D_GDB5 17.798
lower bound upper bound
at level 95% 16.725 19.004
at level 68% 17.145 18.332
Parameter Bayes estimate Credible interval
sD_GDB5 4.53
lower bound upper bound
at level 95% 3.544 5.782
at level 68% 4.028 5.142
----------------------------------------------
Sample name: GDB3
---------------------
Parameter Bayes estimate Credible interval
A_GDB3 46.979
lower bound upper bound
at level 95% 36.343 57.758
at level 68% 40.774 51.082
Parameter Bayes estimate Credible interval
D_GDB3 104.689
lower bound upper bound
at level 95% 96.694 112.104
at level 68% 101.184 108.653
Parameter Bayes estimate Credible interval
sD_GDB3 16.236
lower bound upper bound
at level 95% 9.985 21.678
at level 68% 12.11 18.146
----------------------------------------------
```
**Note:** For an automated parallel processing you can set the argument `jags_method = "rjags"` to `jags_method = "rjparallel"`.
### Remarks
As for the function `Age_computation()`, the age for each sample is set by default between 0.01 ka and 100 ka.
If you have more informations on your samples it is possible to change `PriorAge` parameters.
`PriorAge` is a vector of `size = 2*$Nb_sample`, the two first values of `PriorAge`
concern the 1st sample, the next two values the 2nd sample and so on.
For example, if you know that sample named *GDB5* is a young sample whose its age is between 0.01 ka and 10 ka,
and *GDB3* is an old sample whose age is between 10 ka and 100 ka,
$$PriorAge=c(\underbrace{0.01,10}_{GDB5\ prior\ age},\underbrace{10,100}_{GDB3\ prior\ age})$$
## Age analysis with stratigraphic constraints
With the function `AgeS_Computation()` it is possible to take the stratigraphic
relations between samples into account and define constraints.
For example, we know that *GDB5* is in a higher stratigraphical position, hence it likely has
a younger age than sample *GDB3*.
### Ordering samples
To take into account stratigraphic constraints, the information on the samples need to be ordered.
Either you enter a sample name (corresponding to subfolder names) in `Names` parameter of the function `Generate_DataFile()`, ordered by order of increasing ages or you enter saved .RData informations of each sample in `combine_DataFiles()`, ordered by increasing ages.
``` r
# using Generate_DataFile function
Names <- c("samp1", "samp2")
nbsample <- 2
DATA3 <- Generate_DataFile(
Path = path,
FolderNames = Names,
Nb_sample = nbsample,
verbose = FALSE
)
```
```
Warning in Generate_DataFile(Path = path, FolderNames = Names, Nb_sample = nbsample, : 'Generate_DataFile' est obsolète.
Utilisez plutôt ‘create_DataFile()’.
Voir help("Deprecated")
```
``` r
# using the function combine_DataFiles()
data(DATA1, envir = environment()) # .RData on sample GDB3
data(DATA2, envir = environment()) # .RData on sample GDB5
DATA3 <- combine_DataFiles(L1 = DATA1, L2 = DATA2)
```
### Define matrix to set stratigraphic constraints
Let `SC` be the matrix containing all information on stratigraphic relations for this two samples.
This matrix is defined as follows:
- matrix dimensions: the row number of `StratiConstraints` matrix is equal to `Nb_sample+1`,
and column number is equal to $Nb\_sample$.
- first matrix row: for all $i$ in $\{1,...,Nb\_Sample\}$, `StratiConstraints[1,i] <- 1`,
means that the lower bound of the sample age given in `PriorAge[2i-1]` for the sample whose number ID
is equal to $i$ is taken into account
- sample relations: for all $j$ in $\{2,...,Nb\_Sample+1}\$ and all $i$ in $\{j,...,Nb\_Sample\}$,
`StratiConstraints[j,i] <- 1` if the sample age whose ID is equal to $j-1$ is lower than the sample age whose ID is equal to $i$.
Otherwise, `StratiConstraints[j,i] <- 0`.
To the define such matrix the function *SCMatrix()* can be used:
``` r
SC <- SCMatrix(Nb_sample = 2,
SampleNames = c("samp1", "samp2"))
```
In our case: 2 samples, `SC` is a matrix with 3 rows and 2 columns. The first row contains `c(1,1)` (because we take into account the prior ages), the second line contains `c(0,1)` (sample 2, named *samp2* is supposed to be older than sample 1, named *samp1*) and the third line contains `c(0,0)` (sample 2, named *samp2* is not younger than the sample 1, here named *samp1*). We can also fill the matrix with the stratigraphic relations as follow:
``` r
SC <- matrix(
data = c(1, 1, 0, 1, 0, 0),
ncol = 2,
nrow = (2 + 1),
byrow = T
)
```
### Age computation
``` r
Age <-
AgeS_Computation(
DATA = DATA3,
Nb_sample = 2,
SampleNames = c("samp1", "samp2"),
PriorAge = priorage,
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
StratiConstraints = SC,
Iter = 1000,
jags_method = 'rjags')
```
```
Warning: No initial values were provided - JAGS will use the same initial values for all chains
```
```
Compiling rjags model...
Calling the simulation using the rjags method...
Adapting the model for 1000 iterations...
Running the model for 5000 iterations...
Simulation complete
Calculating summary statistics...
Calculating the Gelman-Rubin statistic for 6 variables....
Finished running the simulation
```
```
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Sample name: samp1
---------------------
Point estimate Uppers confidence interval
A_samp1 1.003 1.005
D_samp1 1 1.002
sD_samp1 1.003 1.009
----------------------------------------------
Sample name: samp2
---------------------
Point estimate Uppers confidence interval
A_samp2 1.004 1.008
D_samp2 1.005 1.017
sD_samp2 1.002 1.01
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
>> Bayes estimates of Age, Palaeodose and its dispersion for each sample and credible interval <<
----------------------------------------------
Sample name: samp1
---------------------
Parameter Bayes estimate Credible interval
A_samp1 9.711
lower bound upper bound
at level 95% 9.126 10
at level 68% 9.677 10
Parameter Bayes estimate Credible interval
D_samp1 29.26
lower bound upper bound
at level 95% 23.914 34.493
at level 68% 26.756 32.052
Parameter Bayes estimate Credible interval
sD_samp1 67.869
lower bound upper bound
at level 95% 51.164 84.839
at level 68% 57.714 74.182
----------------------------------------------
Sample name: samp2
---------------------
Parameter Bayes estimate Credible interval
A_samp2 10.413
lower bound upper bound
at level 95% 10 11.236
at level 68% 10 10.469
Parameter Bayes estimate Credible interval
D_samp2 18.343
lower bound upper bound
at level 95% 17.089 19.48
at level 68% 17.62 18.846
Parameter Bayes estimate Credible interval
sD_samp2 4.619
lower bound upper bound
at level 95% 3.588 5.669
at level 68% 4.003 5.09
----------------------------------------------
```
Thee results can be also be used for an alternative graphical representation:
``` r
plot_Ages(Age, plot_mode = "density")
```
```
SAMPLE AGE HPD68.MIN HPD68.MAX HPD95.MIN HPD95.MAX ALT_SAMPLE_NAME AT
1 samp1 9.711 9.677 10.000 9.126 10.000 NA 2
2 samp2 10.413 10.000 10.469 10.000 11.236 NA 1
```
## When MCMC trajectories did not converge
If MCMC trajectories did not converge, it means we should run additional MCMC iterations.
For `AgeS_computation()` and `Age_OSLC14()` models we can run additional iterations by supplying the function output back into the parent function.
In the following, notice we are using the output of the previous `AgeS_computation()` example, namely `Age`. The key argument to set/change is `DATA`.
``` r
Age <- AgeS_Computation(
DATA = Age,
Nb_sample = 2,
SampleNames = c("GDB5", "GDB3"),
PriorAge = priorage,
distribution = "cauchy",
LIN_fit = TRUE,
Origin_fit = FALSE,
Iter = 1000,
jags_method = "rjags"
)
```
```
Calling the simulation using the rjags method...
Note: the model did not require adaptation
Burning in the model for 4000 iterations...
Running the model for 5000 iterations...
Simulation complete
Calculating summary statistics...
Calculating the Gelman-Rubin statistic for 6 variables....
Finished running the simulation
```
```
>> Results of the Gelman and Rubin criterion of convergence <<
----------------------------------------------
Sample name: GDB5
---------------------
Point estimate Uppers confidence interval
A_GDB5 1 1
D_GDB5 1.001 1.004
sD_GDB5 1.001 1.005
----------------------------------------------
Sample name: GDB3
---------------------
Point estimate Uppers confidence interval
A_GDB3 1.008 1.012
D_GDB3 1.009 1.031
sD_GDB3 1.007 1.026
---------------------------------------------------------------------------------------------------
*** WARNING: The following information are only valid if the MCMC chains have converged ***
---------------------------------------------------------------------------------------------------
>> Bayes estimates of Age, Palaeodose and its dispersion for each sample and credible interval <<
----------------------------------------------
Sample name: GDB5
---------------------
Parameter Bayes estimate Credible interval
A_GDB5 9.724
lower bound upper bound
at level 95% 9.154 10
at level 68% 9.687 10
Parameter Bayes estimate Credible interval
D_GDB5 29.372
lower bound upper bound
at level 95% 23.658 34.505
at level 68% 26.635 32.055
Parameter Bayes estimate Credible interval
sD_GDB5 67.561
lower bound upper bound
at level 95% 50.632 84.409
at level 68% 59.654 76.278
----------------------------------------------
Sample name: GDB3
---------------------
Parameter Bayes estimate Credible interval
A_GDB3 10.406
lower bound upper bound
at level 95% 10 11.176
at level 68% 10 10.468
Parameter Bayes estimate Credible interval
D_GDB3 18.29
lower bound upper bound
at level 95% 17.184 19.532
at level 68% 17.675 18.837
Parameter Bayes estimate Credible interval
sD_GDB3 4.557
lower bound upper bound
at level 95% 3.526 5.591
at level 68% 3.975 5.059
----------------------------------------------
```
# References {-}
Combès, B., Philippe, A., Lanos, P., Mercier, N., Tribolo, C., Guerin, G., Guibert, P., Lahaye, C., 2015.
A Bayesian central equivalent dose model for optically stimulated luminescence dating.
Quaternary Geochronology 28, 62-70. doi: [10.1016/j.quageo.2015.04.001](https://doi.org/10.1016/j.quageo.2015.04.001)
Combès, B., Philippe, A., 2017. Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating. Quaternary Geochronology 39, 24–34. doi: [10.1016/j.quageo.2017.02.003](https://doi.org/10.1016/j.quageo.2017.02.003)
Philippe, A., Guérin, G., Kreutzer, S., 2019. BayLum - An R package for Bayesian analysis of OSL ages: An introduction. Quaternary Geochronology 49, 16-24. doi: [10.1016/j.quageo.2018.05.009](https://doi.org/10.1016/j.quageo.2018.05.009)
## Further reading {-}
### For more details on the diagnostic of Markov chains {-}
Robert and Casella, 2009. Introducing Monte Carlo Methods with R. Springer Science & Business Media.
### For details on the here used dataset {-}
Tribolo, C., Asrat, A., Bahain, J. J., Chapon, C., Douville, E., Fragnol, C., Hernandez, M., Hovers, E., Leplongeon, A., Martin, L., Pleurdeau, D., Pearson, O., Puaud, S., Assefa, Z., 2017. Across the Gap: Geochronological and Sedimentological Analyses from the Late Pleistocene-Holocene Sequence of Goda Buticha, Southeastern Ethiopia. PloS one, 12(1), e0169418.
doi: [10.1371/journal.pone.0169418](https://doi.org/10.1371/journal.pone.0169418)
